Resources tagged with: Generalising

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Broad Topics > Thinking Mathematically > Generalising

Got It

Age 7 to 14
Challenge Level

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

Button-up Some More

Age 7 to 11
Challenge Level

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Games Related to Nim

Age 5 to 16

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

Strike it Out

Age 5 to 11
Challenge Level

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Maths Trails

Age 7 to 14

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

Have You Got It?

Age 11 to 14
Challenge Level

Can you explain the strategy for winning this game with any target?

Sliding Puzzle

Age 11 to 16
Challenge Level

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

More Magic Potting Sheds

Age 11 to 14
Challenge Level

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Dotty Circle

Age 7 to 11
Challenge Level

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

Three Times Seven

Age 11 to 14
Challenge Level

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

Adding in Rows

Age 11 to 14
Challenge Level

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?

Window Frames

Age 5 to 14
Challenge Level

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Broken Toaster

Age 7 to 11 Short
Challenge Level

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

One O Five

Age 11 to 14
Challenge Level

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

Great Granddad

Age 11 to 14
Challenge Level

Great Granddad is very proud of his telegram from the Queen congratulating him on his hundredth birthday and he has friends who are even older than he is... When was he born?

Strike it Out for Two

Age 5 to 11
Challenge Level

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Counting Factors

Age 11 to 14
Challenge Level

Is there an efficient way to work out how many factors a large number has?

Build it Up

Age 7 to 11
Challenge Level

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Got it for Two

Age 7 to 14
Challenge Level

Got It game for an adult and child. How can you play so that you know you will always win?

Picturing Triangular Numbers

Age 11 to 14
Challenge Level

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Number Pyramids

Age 11 to 14
Challenge Level

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

Christmas Chocolates

Age 11 to 14
Challenge Level

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

Repeaters

Age 11 to 14
Challenge Level

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

Train Spotters' Paradise

Age 11 to 16

Dave Hewitt suggests that there might be more to mathematics than looking at numerical results, finding patterns and generalising.

More Twisting and Turning

Age 11 to 16
Challenge Level

It would be nice to have a strategy for disentangling any tangled ropes...

One, Three, Five, Seven

Age 11 to 16
Challenge Level

A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.

Egyptian Fractions

Age 11 to 14
Challenge Level

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

Keep it Simple

Age 11 to 14
Challenge Level

Can all unit fractions be written as the sum of two unit fractions?

Hidden Rectangles

Age 11 to 14
Challenge Level

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Winning Lines

Age 7 to 16

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

Arithmagons

Age 11 to 16
Challenge Level

Can you find the values at the vertices when you know the values on the edges?

Crossings

Age 7 to 11
Challenge Level

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

More Number Pyramids

Age 11 to 14
Challenge Level

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

Partitioning Revisited

Age 11 to 14
Challenge Level

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Enclosing Squares

Age 11 to 14
Challenge Level

Can you find sets of sloping lines that enclose a square?

Three Dice

Age 7 to 11
Challenge Level

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

Centred Squares

Age 7 to 11
Challenge Level

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Special Sums and Products

Age 11 to 14
Challenge Level

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

Surprising Split

Age 7 to 11
Challenge Level

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Nim-like Games

Age 7 to 16
Challenge Level

A collection of games on the NIM theme

Sitting Round the Party Tables

Age 5 to 11
Challenge Level

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Nim-7 for Two

Age 5 to 14
Challenge Level

Nim-7 game for an adult and child. Who will be the one to take the last counter?

Division Rules

Age 7 to 11
Challenge Level

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

Sums and Differences 2

Age 7 to 11
Challenge Level

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Sums and Differences 1

Age 7 to 11
Challenge Level

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Journeys in Numberland

Age 7 to 11
Challenge Level

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Play to 37

Age 7 to 11
Challenge Level

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

Build it up More

Age 7 to 11
Challenge Level

This task follows on from Build it Up and takes the ideas into three dimensions!

What Numbers Can We Make Now?

Age 11 to 14
Challenge Level

Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Squares in Rectangles

Age 11 to 14
Challenge Level

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?